Axis Josephson Junctions with Improved Smoothness

ABSTRACT

According to various implementations of the invention, high quality a-axis XBCO may be grown with low surface roughness. According to various implementations of the invention, low surface roughness may be obtained by: 1) adequate substrate preparation; 2) calibration of flux rates for constituent atoms; and/or 3) appropriate control of temperature during crystal growth. According to various implementions of the invention, a wafer comprises a smoothing layer of c-axis XBCO; a first conducting layer of a-axis XBCO formed on the smoothing layer; an insulating layer formed on the first conducting layer; and a second conducting layer of a-axis XBCO formed on the insulating layer, where, for a same surface roughness, a thickness of the smoothing layer and the first conducting layer combined is greater than a thickness of the first conducting layer without the smoothing layer. According to various implementations of the invention, a Josephson Junction is etched out of the XBCO/insulating layer/XBCO trilayer by: ion mill etching the top XBCO layer and some of the insulating layer to intentionally leave some of the insulating layer on the bottom XBCO layer; and/or ion mill etching at least the insulating layer at an off angle to reduce or minimize ion damage to the bottom XBCO layer otherwise introduced by the ion mill.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 63/219,417, entitled “A-axis Josephson Junctions with ImprovedSmoothness,” filed on Jul. 8, 2021, which is incorporated herein byreference in its entirety.

FIELD OF THE INVENTION

The invention is generally related to Josephson Junctions, and morespecifically, to techniques for manufacturing Josephson Junctions froma-axis YBCO with improved smoothness.

BACKGROUND OF THE INVENTION

Recently, employing YBCO materials in an a-axis crystalline orientationhave become desirable, including for fabricating Josephson Junctions. Inorder to simplify fabrication of a-axis Josephson Junctions (as well asother circuits employing a-axis materials), thick layers (e.g., greaterthan 100 nm) of a-axis materials and low surface roughness (e.g., lessthan 1 nm) are desired. However, researchers have found a positivecorrelation between thickness of certain a-axis materials and theirsurface roughness (also sometimes described as surface smoothness). Forexample, a-axis materials having a thickness of 100 nm had a surfaceroughness of 2 nm, with the surface roughness increasing as thethickness increased.

Increased thickness of a-axis materials with improved (i.e., lower)surface roughness are needed.

SUMMARY OF THE INVENTION

According to various implementions of the invention, a wafer comprises asmoothing layer of c-axis XBCO; a first conducting layer of a-axis XBCOformed on the smoothing layer; an insulating layer formed on the firstconducting layer; and a second conducting layer of a-axis XBCO formed onthe insulating layer, where, for a same surface roughness, a thicknessof the smoothing layer and the first conducting layer combined isgreater than a thickness of the first conducting layer without thesmoothing layer.

According to various implementations of the invention, a-axis thin filmYBCO layers may be deposited using a technique called molecular beamepitaxy (MBE). MBE is a well-characterized crystal growth technique forimproved thin films in the semiconductor domain. According to variousimplementations of the invention, MBE may be used to grow very highquality YBCO (and similar materials) thin films in an a-axis crystalorientation. Various implementations of the invention provide highercrystalline quality, higher accuracy in film thickness, higher a-axisorientation, as well as single crystal growth with lattice matching orstrained lattice matching with YBCO-related thin film materials.

Various implementations of the invention utilize various perovskitematerials including, but not limited to, YBa₂Cu₃O_(7-x),PrBa₂Cu₃O_(7-x), DyBa₂Cu₃O_(7-x), NdBa₂Cu₃O_(7-x), and otherperovskites, which are commonly referred to as simply YBCO, PBCO, DBCO,NBCO, etc., respectively, as would be appreciated. Such materials maycommonly and collectively be expressed as XBa₂Cu₃O_(7-x) (XBCO) where Xcan be elements such as Y, Pr, Dy, Nd, etc., as would be appreciated.

According to various implementations of the invention, high qualitya-axis XBCO may be grown with low surface roughness. “Surface roughness”may be generally described as deviations in the direction of a normalvector of an actual surface(s) of the material from an ideal surface.

According to various implementations of the invention, achieving lowsurface roughness in a-axis XBCO may be obtained by: 1) adequatesubstrate preparation; 2) calibration of MBE flux; and 3) appropriatecontrol of temperature during crystal growth.

These and other features of the invention are described in detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates Josephson Junction component layers having twoconducting layers and an insulating layer between the conducting layersaccording to various implementations of the invention.

FIG. 2 illustrates a wafer of Josephson Junction component layers on topof a smoothing layer according to various implementations of theinvention.

FIG. 3 illustrates an a-axis Josephson Junction according to variousimplementations of the invention.

FIG. 4 illustrates a smoothing layer in between stacked JosephsonJunction component layers according to various implementations of theinvention.

FIG. 5 illustrates multiple a-axis Josephson Junctions according tovarious implementations of the invention.

FIG. 6 illustrates a wafer of Josephson Junction component layers on topof a smoothing layer, with a transition layer disposed in between,according to various implementations of the invention.

FIG. 7 illustrates a superlattice according to various implementationsof the invention.

FIG. 8 illustrates a growth temperature profile according to variousimplementations of the invention.

FIGS. 9A-9G illustrate YBCO/PBCO/YBCO trilayers grown on a substratesand their associated RHEED images.

FIGS. 10A-10C generally illustrate x-ray diffraction of YBCO/PBCO/YBCOtrilayers.

FIGS. 11A-11E generally illustrate surface morphology of theYBCO/PBCO/YBCO trilayers as revealed by AFM.

FIGS. 12A-12C generally illustrate transport properties of theYBCO/PBCO/YBCO trilayers.

FIGS. 13A-13G generally illustrate cross-sectional high-resolution STEMimages that reveal a microstructure and interface abruptness of theYBCO/PBCO/YBCO trilayers.

FIGS. 14A-14D generally illustrate growth of a CuO calibration film.

FIGS. 15A-15C generally illustrate growth of a BaO calibration film.

FIGS. 16A-16D generally illustrate growth of a Y₂O₃ calibration film.

FIGS. 17A-17D generally illustrate growth of a PrO₂ calibration film.

FIGS. 18A-18D generally illustrate off-axis ϕ scans of the 102 family ofpeaks for different thicknesses of YBCO/PBCO/YBCO trilayers.

FIGS. 19A-19F generally illustrate a temperature ramping procedure andrelated RHEED patterns.

FIGS. 20A-20D generally illustrate cross-sectional high-resolution STEMimages that reveal a microstructures of YBCO/PBCO/YBCO trilayers.

FIGS. 21A-21B generally illustrate XRD scans of a less-idealYBCO/PBCO/YBCO trilayer.

FIG. 22 generally illustrates cross-sectional high-resolution STEMimages of a less-ideal YBCO/PBCO/YBCO trilayer.

FIGS. 23A-23G generally illustrate a low-magnification cross-sectionalhigh-resolution STEM images of a less-ideal YBCO/PBCO/YBCO trilayer.

FIG. 24 illustrates an R-T curve for a top layer of YBCO (in aYBCO/PBCO/TBCO trilayer) confirming presence of a critical temperature,T_(c), and hence, transition of this layer of YBCO to a superconductingstate, according to various implementations of the invention.

FIG. 25 illustrates an I-V curve confirming operation for each of twoJosephson Junctions under test, according to various implementations ofthe invention.

FIG. 26 illustrates an ideal I-V curve for an operating JosephsonJunction as would be appreciated.

FIGS. 27A-27B illustrate initial and final testing configurations foroperation of the Josephson Junctions in accordance with variousimplementations of the invention.

DETAILED DESCRIPTION

Various implementations of the invention utilize various perovskitematerials including, but not limited to, YBa₂Cu₃O_(7-x),PrBa₂Cu₃O_(7-x), DyBa₂Cu₃O_(7-x), NdBa₂Cu₃O_(7-x), and otherperovskites, which are commonly referred to as simply YBCO, PBCO, DBCO,NBCO, etc., respectively, as would be appreciated. Such materials maycommonly and collectively be expressed as XBa₂Cu₃O_(7-x) (XBCO) where Xcan be elements such as Y, Pr, Dy, Nd, etc., as would be appreciated.

According to various implementations of the invention, molecular beamepitaxy (MBE) may be used to grow very high quality XBCO thin films inan a-axis crystal orientation, though other processes for growing a-axisXBCO may be used as would be appreciated. Various implementations of theinvention provide higher crystalline quality, higher accuracy in filmthickness, higher a-axis orientation, as well as single crystal growthwith lattice matching or strained lattice matching with XBCO-relatedthin film materials.

According to various implementations of the invention, high qualitya-axis XBCO may be grown with low surface roughness. “Surface roughness”may be generally described as deviations in the direction of a normalvector of an actual surface(s) of the material from an ideal surface.One mechanism for achieving low surface roughness for a-axis XBCO isdescribed in U.S. Provisional Patent Application No. 63/035,162, havinga filing date of Jun. 5, 2020, and entitled “Forming A-axis YBCO byMolecular Beam Epitaxy,” which is one of the priority applicationsincorporated above, and now described.

Various implementations of the invention are directed toward growinghigh quality a-axis XBCO on substrates. While various implementations ofthe invention are described as useful for growing high quality a-axisXBCO, such implementations may be used for growing high quality a-axisYBCO, or other perovskites, as would be appreciated.

For purposes of this description, “surface roughness” may be used toassess a quality of the a-axis XBCO, with lower measures of surfaceroughness being generally preferable to higher measures of roughness.Other measures may be used to assess a quality of a-axis XBCO as wouldbe appreciated. In some implementations of the invention, surfaceroughness is less than 10 nm. In some implementations of the invention,surface roughness is less than 2 nm. In some implementations of theinvention, surface roughness is less than 1.5 nm In some implementationsof the invention, surface roughness is less than 0.5 nm.

According to various implementations of the invention, high qualitya-axis XBCO may be obtained by: 1) adequately preparing a substrate; 2)calibrating MBE flux; and 3) controlling temperature during crystalgrowth. Each of these is described below.

According to various implementations of the invention, adequatelypreparing a substrate for subsequent XBCO crystal growth may beimportant for producing high quality a-axis XBCO. A “smooth” substrate(i.e., a substrate with low roughness) ensures a smoother XBCO surface.According to various implementations of the invention, reflectionhigh-energy electron diffraction (RHEED) may be used to characterize thesurface of the substrate. According to various implementations of theinvention, a smooth substrate surface will produce clear RHEED patternsand ultimately, a smooth XBCO surface.

In some implementations of the invention, lanthanum aluminate (LaAlO₃ orcommonly referred to as LAO) may be used a a substrate. LAO is aninorganic, ceramic oxide with a distorted perovskite structure. Othersimilar materials may be used as the substrate as would be appreciated.

In some implementations of the invention, the substrate may have auniformly terminated, atomically smooth surface. In some implementationsof the invention, LAO may be terminated with aluminum oxide (AlO₂) forstability. In some implementations, LAO may be terminated with AlO₂ asdescribed in J. R. Kim et al., “Experimental realization of atomicallyflat and AlO₂-terminated LaAlO₃ (001) substrate surfaces,” Phys. Rev.Mater., vol. 3, no. 2, pp. 1-8, 2019 (“Kim”), which was included asAppendix A in U.S. Provisional Application No. 63/035,162, which is oneof the priority applications incorporated above. Kim outlines a processfor removing lanthanum and creating a smooth aluminum oxide surface.

In some implementations, the substrate may be etched in boiling water,annealed at 1300° C. in air for 10 hours, and then etched again inboiling water, to obtain an AlO₂-terminated surface with astep-and-terrace morphology.

In some implementations of the invention, terminating the LAO to producethe AlO₂ surface may be accomplished by annealing the LAO substrate at1200° C. under oxygen for nominally three hours and then sonicating theannealed LAO substrate in deionized water for nominally two hours.

In some implementations of the invention, LAO may be terminated withlanthanum oxide (La₂O₃) for stability as would be appreciated. In someimplementations of the invention, LAO may be terminated with somemixture of aluminum oxide and lanthanum oxide as would be appreciated.

According to various implementations of the invention, calibratingatomic flux rates in the MBE may be may be important for producing highquality a-axis XBCO. For example when XBCO is YBCO, precise control offlux rates for each of yttrium, barium and copper atomic may beimportant for producing high quality a-axis YBCO. In such crystals,there are one yttrium and two barium atoms for every three copper atoms,so the incoming rate of atoms should be precisely set and controlled tothese ratios (i.e., a rate of flux of yttrium is one third of a rate offlux of copper, and a rate of flux of barium is two thirds of the rateof flux of copper). Other ratios may be used when rare earth metalsother than yttrium are used as would be appreciated.

In some implementations of the invention, stoiciometric flux calibrationmay be used as would be appreciated. In some implementations of theinvention, RHEED or atomic absorption spectroscopy may be used tomeasure an incoming rate of the respective atoms.

In some implementations of the invention, a four-step calibrationprocess may be used to calibrate atomic flux rates in the MBE. In afirst step, fluxes of each of the constituent atoms are tuned near theirtarget stoichiometric ratios using standard flux monitoring tools, suchas a quartz crystal microbalance (QCM), a beam flux monitor (BFM), orother flux monitoring tools as would be appreciated. This first step maybe referred to as a “coarse calibration.”

In a second step, or “fine calibration,” because each constituent atomof YBCO (yttrium, barium, copper) has an easy-to-form binary oxide(e.g., Y₂O₃, BaO and/or BaO₂, CuO and/or Cu₂O, etc.), such binary oxidesmay be grown sequentially on lattice-matched substrates or buffer layers(e.g., Y₂O₃ on YSZ, BaO or BaO₂ on STO, CuO or Cu₂O on MgO) inconditions similar to those used to ultimately grow YBCO. During thisfine calibration, in-situ RHEED and ex-situ X-ray reflectivity mayprovide very precise measurements of growth rate of these binary oxideswhich can be used to determine precise flux values using the standardlattice constants of the films and substrates as would be appreciated.Similar fine calibration using other binary oxides may be used when rareearth metals other than yttrium are used as would be appreciated.

In a third step, coarse calibration and fine calibration are repeateduntil the target flux ratios are obtained. In some implementations ofthe invention, the flux rate for one of constituent atoms may be set,and then the flux rate(s) of the remaining constituent atom(s) may beiteratively tuned to their corresponding flux ratio. In someimplementations of the invention, a flux rate of copper may be set, andthen flux rates of yttrium and barium may be iteratively tuned to onethird and two thirds of copper, respectively.

In a fourth step, a calibration test sample of XBCO may be completed ona small scale, such as a 1 cm×1 cm substrate. In some implementations,the calibration test sample may be analyzed via ex-situ x-raydiffraction (XRD), which may provide information regarding thecomposition and quality of the calibration test sample as measured, forexample, by standard tools such as atomic force microscope (AFM),transmission electron microscopy (TEM), scanning electron microscope(SEM), etc. In some implementations, the calibration test sample may beanalyzed via in-situ x-ray photoelectron spectroscopy (XPS), which mayprovide information regarding the composition and quality of thecalibration test sample. Other techniques that will providecompositional information may be Rutherford backscatter spectrometery(RBS), electron energy loss spectroscopy (EELS), electron dispersivex-ray spectroscopy (EDX), etc. Based on the composition of thecalibration test sample, any of the foregoing steps may be repeated tofurther fine tune the flux rates.

According to various implementations of the invention, controllingtemperature during crystal growth during MBE may be may be important forproducing high quality a-axis XBCO. In some implementations of theinvention, a positive temperate ramp may be desirable during crystalgrowth. In some implementations of the invention, starting crystalgrowth at a low temperature may force XBCO crystals to form in thea-axis orientation. In some implementations of the invention, slowlyincreasing temperature maintains the a-axis orientation of the XBCOcrystals while improving crystal quality and material properties,including, but not limited to, superconducting properties.

FIG. 8 illustrates a growth temperature profile 800 according to variousimplementations of the invention. Growth temperature profile 800 plots achamber temperature against a thickness of XBCO. During a first profileportion 810 of profile 800, optimized a-axis XBCO may be grown as a thintemplate layer at an initial temperature. In some implementations of theinvention, this initial temperature may be in the range 400-500° C.; insome implementations of the invention, this initial temperature may bein the range 400-440° C.; in some implementations of the invention, thisinitial temperature may be in the range 410-430° C.; in someimplementations of the invention, this initial temperature may benominally 420° C.; other initial temperatures or temperature ranges maybe used as would be appreciated. In some implementations of theinvention, this thin template layer may be less than 20 nm in thickness;in some implementations of the invention, this thin template layer maybe 10-20 nm in thickness; in some implementations of the invention, thisthin template layer may be 1-10 nm in thickness; in some implementationsof the invention, this thin template layer may be 1-5 nm in thickness;other thicknesses may be used as would be appreciated.

During a second profile portion 820, the chamber temperature may beramped to an intermediate temperature without otherwise changing ordisrupting crystal growth. In some implementations of the invention, thechamber temperature may be ramped to the intermediate temperature at atemperature ramp rate. In some implementations of the invention, theintermediate temperature may be 505° C., though other intermediatetemperatures may be used as would be appreciated. In someimplementations of the invention, the temperature ramp rate may be 10°C./nm, although the temperature ramp rate may range from 0.5° C./nm to30° C./nm; other temperature ramp rates may be used, including varyingtemperature ramp rates, different temperature ramp rates, etc., as wouldbe appreciated. In some implementations of the invention, thetemperature ramp rate may be linear; in some implementations of theinvention, the temperature ramp rate may be sublinear; or in someimplementations of the invention, the temperature ramp rate may besuperlinear. In some implementations of the invention, the temperatureramp may be non-linerar. In some implementations of the invention, thetemperature ramp may vary in stepwise fashion. In some implementationsof the invention, the temperature may be a combination of any of theabove.

During a third profile portion 830, beginning when the chambertemperature reaches the intermediate temperature and ending when thechamber temperature reaches a final growth temperature, the fluxes ofthe constituent atoms of XBCO (i.e., X, B, C) are turned off with onlyoxygen remaining on. In some implementations of the invention, thechamber temperature may be adjusted to the final growth temperature. Insome implementations of the invention, the chamber temperature may beramped to the final growth temperature at a second temperature ramprate. In some implementations of the invention, the second temperatureramp rate may be the same or nominally similar to the temperature ramprate during second profile portion 820; though other second temperatureramp rates may be used as would be appreciated. In some implementationsof the invention, the final growth temperature may be 570° C., thoughother final growth temperatures or ranges of final growth temperaturesmay be used as would be appreciated.

During a fourth profile portion 840, beginning when the chambertemperature reaches the final growth temperature, the fluxes of theconstituent atoms of XBCO (i.e., X, B, C) are turned backed on. In someimplementations of the invention, the chamber temperature remainsconstant at the final growth temperature until a desired thickness ofXBCO is obtained as would be appreciated.

In some implementations of the invention, once the desired thickness ofXBCO is obtained, a layer of X₂BCO may be grown on top of the XBCO,where X₂ may be different from X. For example, a layer of PBCO may begrown on top of a layer of YBCO. In this example, PBCO may be grown ontop of YBCO by exchanging the flux of yttrium with a flux ofpraseodymium. Further alternating layers or differing layers may begrown as would be appreciated.

Table 1 compares a-axis YBCO grown in accordance with variousimplementations of the invention with a-axis YBCO grown as described inthe following papers: 1) Takeuchi et al., “Fabrication of in-planealigned a-axis oriented YBa2Cu3O7-x trilayer Josephson junctions,” Appl.Phys. Lett., vol. 69, no. 1, pp. 112-114, 1996; 2) Trajanovic, et al.,“Oxygen pressure dependence of the grain size and surface morphology inYBa 2 Cu 3 O 7-x a-axis films,” Appl. Phys. Lett., vol. 66, no. 12, pp.1536-1538, Mar. 1995; 3) Takeuchi et al., “Fabrication of all in-planeoriented a-axis YBa 2 Cu 3 O 7-x/insulator/YBa 2 Cu 3 O 7-xheterostructures,” Appl. Phys. Lett., vol. 66, no. 14, pp. 1824-1826,Apr. 1995; and 4) Trajanovic, et al., “Growth Optimization andCharacterization of a-axis Oriented Y—Ba—Cu—O Thin Films on (100)LaSrGa04 Substrates,” IEEE Trans. Appl. Supercond., vol. 5, no. 2, pp.1237-1240, 1995. Each of these papers was included in Appendix B of U.S.Provisional Application No. 63/035,162, which is one of the priorityapplications incorporated above. For purposes of clarity, these papersdescribe growing samples of YBCO in PLD on SLGO substrates.

TABLE 1 Comparision of Results YBCO-Takeuchi YBCO-Aspects Measurement[1]-[4] of Invention Roughness 5 nm @ 380 nm 0.63 nm @ 40 nm thicknessthickness Transition 85K @ 50 nm 89K @ 50 nm Temperature % a-axisby >95% (beyond >95% (in some XRD instrument precision) cases >99%)

FIG. 1 illustrates Josephson Junction (JJ) component layers 100 usefulfor describing various implementations of the invention. In variousimplementations of the invention, JJ component layers 100 may includetwo conducting layers 110 of a-axis X₁BCO (Illustrated in FIG. 1 as aconducting layer 110A and a conducting layer 110B) and an insulatinglayer 120 of X₂BCO between conducting layers 110. In someimplementations, X₂BCO may be oriented along an a-axis (i.e., a-axisX₂BCO) or oriented along another axis as would be appreciated. In someimplementations, X₁ and X₂ are different elements (and hence, X₁BCO andX₂BCO are different materials) as would be appreciated. In someimplementations, X₁ and X₂ are the same element, though X₁BCO and X₂BCOare arranged in different orientations (e.g., one a-axis and one c-axis,etc.). In some implementations, X₁ and X₂ are the same element, thoughX₁BCO and X₂BCO are arranged in the same general orientation, but withdifferent angular offsets (e.g., one a-axis with 0° offset and onea-axis with 30° offset, etc.). In some implementations, each conductinglayer 110 comprises a-axis YBCO and insulating layer 120 comprises PBCO,though other conducting layers and/or insulating layers may be used aswould be appreciated. In some implementations, each conducting layer 110comprises a-axis YBCO and insulating layer 120 comprises a-axis PBCO,though other conducting layers, insulating layers, and/or orientationsmay be used as would be appreciated.

As discussed above, thick conducting layers 110 are desired tofacilitate fabrication of JJ components 100 with other semiconductorcomponents using conventional semiconductor processes. For example, insome implementations, conducting layer 110A may have a desired thicknessof 100 nm, or more. However, increasing the thickness of layers ofa-axis XBCO (e.g., YBCO) often results in increasing surface roughness.For example, surface roughness of a-axis YBCO exceeds 2 nm forthicknesses of 100 nm, or more. Such surface roughness may not beconducive for fabricating JJ components 100 with other stackedsemiconductor components.

Various implementations of the invention, in order to achieve, ineffect, thicker layers of conducting layer 110A, employ an initialsmoothing layer of c-axis XBCO beneath conducting layer 110A. C-axisXBCO does not suffer from increases in surface roughness as thicknessincreases to the degree that a-axis XBCO does. Thus, thicker layers ofc-axis XBCO may be used to achieve a given surface roughness as comparedwith layers of a-axis XBCO.

FIG. 2 illustrates a wafer 200 including JJ component layers 100 layeredon top of a smoothing layer 220 and a substrate 210 according to variousimplementations of the invention. According to the invention, smoothinglayer 220 may be used to increase an effective thickness of conductinglayer 110A (i.e., a combined thickness of smoothing layer 220 andconducting layer 110A) without increasing surface roughness ofconducting layer 110A. In some implementations of the invention,smoothing layer 220 comprises c-axis X₁BCO. In some implementations ofthe invention smoothing layer 220 comprises c-axis X_(n)BCO, where X₁and X_(n) are different elements (and hence X₁BCO and X_(n)BCO aredifferent materials). In general, smoothing layer 220 may have athickness of 1 nm to 1 μm, or more.

In some implementations of the invention, smoothing layer 220 maypatterned, for example, via post-epitaxial etching, as a wiring layer asan added benefit. In implementations, where smoothing layer 220comprises c-axis XBCO, superconducting currents may optimally flow inboth horizontal directions, whereas in a-axis XBCO, superconductingcurrents optimally flow in only one horizontal direction along with avertical direction as would be appreciated.

FIG. 3 illustrates an a-axis Josephson Junction 300 according to variousimplementations of the invention. As illustrated, wafer 200 is etched(and more specifically, JJ component layers 100 of wafer 200 are etched)to partially reveal smoothing layer 220. Further processing lays down aterminal pad 310A on smoothing layer 220 and a terminal pad 310B onconducting layer 110B to provide electrical connections for a-axisJosephson Junction 300. According to various implementations of theinvention, when in use, current applied to terminal pad 310A flowsthrough smoothing layer 220 to conducting layer 110A, through conductinglayer 110A, across insulating layer 120, and through conducting layer110B to terminal pad 310B.

FIG. 4 illustrates a stack 400 of JJ component layers 100 (illustratedas JJ component layers 100A and JJ component layers 100B) with anadditional smoothing layer 220B disposed in between them according tovarious implementations of the invention. According to variousimplementations of the invention, any surface roughness found on top offirst JJ component layers 100A may be reduced using smoothing layer 220Bin preparation for second JJ component layers 100B. In this way, surfaceroughness introduced by each JJ component layers 100 are not cumulativethrough a given stack and may be mitigated by introducing intermediatesmoothing layers 220 as would be appreciated.

FIG. 5 illustrates an example stacked device 500 of a-axis JosephsonJunctions according to various implementations of the invention. Asillustrated, stack 400 is etched to partially reveal smoothing layer220A and smoothing layer 220B. Further processing lays down a terminalpad 310A on smoothing layer 220A, a terminal pad 310B on smoothing layer220B, and a terminal pad 310C on top of JJ component layers 100B toprovide electrical connections for two a-axis Josephson Junctions. Otherconfigurations and numbers of Josephson Junctions may be used as wouldbe appreciated.

FIG. 6 illustrates a wafer 600 of JJ component layers 100 on top of asmoothing layer 220, with a transition layer 610 disposed in between JJcomponent layers 100 and smoothing layer 220, according to variousimplementations of the invention. In some implementations of theinvention, transition layer 610 comprises a mix of materials, or mix ofmaterial orientations, as the respective layers transistion betweensmoothing layer 220 (e.g., a layer of c-axis XBCO) and conducting layer110A (e.g., a layer of a-axis XBCO). In some implementations of theinvention, transistion layer 610 may have a thickness of approximately 1nm; though in other implementations, transistion layer 610 may have athickness of 20 nm or more, depending on quality of growth of thematerials as would be appreciated. In some implementations, transitionlayer 610 may provide passive electrical functions, such as impedanceand/or capacitance as would be appreciated.

In some implementations of the invention, a superlattice 700 comprisedof different layers 710 of materials may be constructed as illustratedin FIG. 7 . In some implementations, superlattice 700 may be used inplace of any layer or combination of layers referenced above. In someimplementations of the invention, superlattice 700 may comprise anynumber of layers 710A formed in a pattern alternating between layer 710Aand layer 710B. While illustrated as having alternating layers 710 oftwo different materials, such configuration of superlattice 700 is notnecessary, and any number of different and/or alternating layers 710 orpatterns of layers 710 may be used as would be appreciated. In someimplementations of the invention, superlattice 700 may comprise anynumber of the same or different insulating layers 710. In someimplementations of the invention, superlattice 700 may comprise anynumber of the same or different conducting layers 710. In someimplementations of the invention, superlattice 700 may comprise anynumber of insulating and/or conducting layers 710 as would beappreciated. In some implementations, layers 710 may have a thickness of1 nm to 50 nm or more, as would be appreciated.

In some implementations, layer 710A may be comprised of X_(a)BCO andlayer 710B may be comprised of X_(b)BCO. In some implementations, anynumber of different layers 710 may be used, each comprised of adifferent X_(a)BCO, repeating in pattern or otherwise. In someimplementations, X_(a)BCO is a different material than X_(b)BCO (and/orX_(i)BCO, etc., as the case may be); for example, where X_(a) is adifferent element that X_(b) (and/or X_(i), etc.). In someimplementations, X_(a)BCO and X_(b)BCO (and/or X_(i)BCO, etc., as thecase may be) may be the same material in a different orientation fromone another; for example, where X_(a)BCO is a material oriented in thea-axis and X_(b)BCO is the same material oriented in the b-axis, orwhere X_(a)BCO is a material oriented in the b-axis and X_(b)BCO is thesame material oriented in the c-axis, or where X_(a)BCO is a materialoriented in the a-axis and X_(b)BCO is the same material oriented in thec-axis. In some implementations, X_(a)BCO and X_(b)BCO (and/or X_(i)BCO,etc., as the case may be) may be the same material in a similarorientation with one another, but with a different offset; for example,where X_(a)BCO is a material oriented along the a-axis with a 0° offsetand X_(b)BCO is the same material oriented along the a-axis with a 30°offset, or other offset as would be appreciated. In someimplementations, X_(a)BCO and X_(b)BCO (and/or X_(i)BCO, etc., as thecase may be) may be the same material with a different stoichiometryfrom one another. In some implementations, any combination of theforegoing differences between X_(a)BCO and X_(b)BCO may be used to formsuperlattice 700; for example, layer 710A may comprise a-axis X_(a)BCOand layer 710B may comprise c-axis X_(b)BCO, where in addition todifferent orientations, elements X_(a) and X_(b) are also differentelements. Other combinations of layers may be used as would beappreciated.

Example 1

To achieve the desired Y(Pr):Ba:Cu=1:2:3 composition ratio in thedeposited Y(Pr)Ba₂Cu₃O_(7-x) films, these elements are assumed to have asticking coefficient of unity for the growth conditions used forY(Pr)Ba₂Cu₃O_(7-x). Under this assumption, the individual fluxes ofyttrium, praseodymium, barium, and copper are established bysynthesizing epitaxial films of their respective binary oxidesindividually, and either x-ray reflectivity (XRR) or RHEED oscillationsare used to determine the thicknesses of these calibration films. Fromthe measured film thickness and assuming (1) unity sticking coefficientsof these cations for the growth conditions used to grow the binary oxidecalibration films and (2) that these calibration films are fully relaxedand have the bulk density of these binary oxides, the respectiveelemental fluxes are calculated. Having established the elemental fluxesunder the assumptions stated, the temperatures of the MBE effusion cellscontaining yttrium, praseodymium, barium, and copper are adjusted untilthe binary oxide calibration films grown with these sources indicatethat the desired 1:2:3 flux ratio among Y(Pr):Ba:Cu. At this point, thegrowths of Y(Pr)Ba₂Cu₃O_(7-x) andYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers commence. Thesebinary oxide flux calibrations may be performed each day, immediatelyprior to the growth of Y(Pr)Ba₂Cu₃O_(7-x)andYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers to achievethe growth of stoichiometric films. The demonstrated success in growingphase-pure Y(Pr)Ba₂Cu₃O_(7-x) thin films andYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers attests to thevalidity of the assumptions made in this calibration procedure.

The conditions used to grow each of the binary oxides—Y₂O₃, PrO₂, BaO,and CuO—are outlined in Table 2. Also shown are the substrates used andepitaxial orientations of the resulting binary oxide calibration films.In all cases, the oxidant used is distilled ozone (˜80% O₃+20% O₂),i.e., the same oxidant and background pressure used for the growth ofthe subsequent Y(Pr)Ba₂Cu₃O_(7-x) thin films andYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers. For Y₂O₃, PrO₂,and CuO the thickness of the calibration film is measured by XRR. Forhydroscopic BaO, the RHEED oscillation periodicity corresponding to thesmallest charge-neutral formula unit of BaO, which in the case of BaO ishalf of the cubic lattice constant of BaO, is used to calculate thebarium flux. Examples of the RHEED patterns, RHEED oscillations, XRD θ⁻²θ scans, and XRR scans for this calibration method are illustrated foreach binary oxide in FIGS. 14-17 . The orientation relationships of thebinary oxide calibration layers are: (111) Y₂O₃ ∥ (111) YSZ and [ 1 10]Y₂O₃ ∥ [ 1 10] YSZ, (111) PrO₂ ∥ (111) YSZ and [ 1 10] PrO₂ ∥ [ 1 10]YSZ, (100) BaO ∥ (100) SrTiO₃ and [100] BaO ∥ [110] SrTiO₃, and (111)CuO ∥ (100) MgO and [ 1 10] CuO ∥ [ 1 10] MgO.(YSZ=(ZrO₂)_(0.905)(Y₂O₃)_(0.905) (or 9.5 mol % yttria-stabilizedzirconia.))

TABLE 2 Binary Growth Conditions Temperature Pressure Binary oxideSubstrate (° C.) (Torr) (111) CuO (100) MgO Room Temperature 1 × 10⁻⁶(100) BaO (100) SrTiO₃ 600 1 × 10⁻⁶ (111) Y₂O₃ (111) YSZ 900 1 × 10⁻⁶(111) PrO₂ (111) YSZ 900 1 × 10⁻⁶

FIGS. 14A-14D generally illustrate growth of a CuO calibration film.FIGS. 14A and 14B illustrate RHEED patterns along the [110] and [100]azimuths of MgO. FIG. 14C illustrates θ-2θ XRD scan and FIG. 14Dillustrates x-ray reflectivity scan. The example illustrated correspondsto a 12.2 nm thick CuO calibration film.

FIGS. 15A-15C generally illustrate growth of a BaO calibration film.FIGS. 15A and 15B illustrate RHEED patterns along the [110] and [100]azimuths of SrTiO₃. FIG. 15C illustrates RHEED oscillations of thediffracted streak from the outline red box showing layer-by-layergrowth. The example illustrated corresponds to a 7 nm thick BaOcalibration film.

FIGS. 16A-16C generally illustrate growth of a Y₂O₃ calibration film.FIG. 16A and FIG. 16B illustrate RHEED patterns along the [ 1 10] and [21 1 ] azimuths of YSZ. FIG. 16C illustrates a θ⁻² θ scan and FIG. 16Dillustrates a x-ray reflectivity scan. The example illustratedcorresponds to a 11.5 nm thick Y₂O₃ calibration film.

FIGS. 17A-17D generally illustrate growth of a PrO₂ calibration film.FIG. 17A and FIG. 17B illustrate RHEED patterns along the [ 1 10] and [21 1 ] azimuths of YSZ. FIG. 17C illustrates a θ⁻² θ scan and FIG. 17Dillustrates a x-ray reflectivity scan. The example illustratedcorresponds to a 11.1 nm thick PrO₂ calibration film.

FIGS. 18A-18D generally illustrate off-axis ϕ scans of the 102 family ofpeaks at χ=56.8° (red) and χ=33.2° (blue). FIG. 18A illustrates a scanfor 24 nm/8 nm/24 nm YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)trilayers; FIG. 18B illustrates a scan for 32 nm/8 nm/32 nmYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers; FIG. 18Cillustrates a scan for 64 nm/8 nm/64 nmYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers; and FIG. 18Dillustrates a scan for 100 nm/8 nm/100 nmYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers. Peak areaintegration indicates that the volume fractions of a-axis orientedY(Pr)Ba₂Cu₃O_(7-x) in these trilayers are 97%, 97%, 96%, and 99%,respectively.

FIGS. 19A-19F generally illustrate the temperature ramping procedure andrelated RHEED patterns. FIG. 19A illustrates a four-steptemperature-ramping method for the growth of theYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers. FIG. 19Billustrates a schematic of the YBa₂Cu₃O_(7-x) layer grown on a (100)LaAlO₃ substrate. Real-time RHEED images of a single YBa₂Cu₃O_(7-x)layer acquired at four different temperatures during the temperatureramping procedure, i.e., at thermocouple temperatures of T_(Tc)=440° C.(FIG. 19C), T_(Tc)=470° C. (FIG. 19D), T_(Tc)=500° C. (FIG. 19E), andT_(Tc)=540° C. (FIG. 19F). The red arrows added to FIGS. 19C-19F pointto the diffraction streaks associated with the c-axis of theYBa₂Cu₃O_(7-x) lying in-plane. As the temperature is ramped, thesestreaks become more intense and sharper, demonstrating the enhancedcrystalline quality of the a-axis oriented YBa₂Cu₃O_(7-x) film duringgrowth.

FIG. 20A illustrates a representative cross-sectional HAADF-STEM imageof the 24 nm/8 nm/24 nm YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)trilayer highlighting aspects of the microstructure observed. The six(1-6) pink circles indicate the positions at which the RHEED patternspresented in FIG. 9A were taken during growth. The thickness of thecubic (Y,Ba)CuO_(3-x) buffer layer is 10±2 nm. FIG. 20B illustrates ahigh-magnification HAADF-STEM image showing the region of interesthighlighted by the green rectangle in FIG. 20A. The orange arrowindicates the intercalation of an additional CuO layer (dark feature) asa consequence of YBa₂Cu₄O_(8-x) stacking faults with double-chainlayers. FIG. 20C illustrates the high magnification view of the areahighlighted by the gray rectangle in FIG. 20A and demonstrates thepresence of YBa₂Cu₃O_(7-x) and PrBa₂Cu₃O_(7-x) in-plane rotation twinson top of the cubic (Y,Ba)CuO_(3-x) layer that forms during the “cold”growth. The gray double-sided arrows mark the width of the 90° in-planerotational twins. FIG. 20D illustrates the high magnification view ofthe area highlighted by the pink rectangle in FIG. 20A and shows theboundary between the cubic (Y,Ba)CuO_(3-x) and the a-axis YBa₂Cu₃O_(7-x)layer, marked by the pink line.

FIGS. 21A-21B generally illustrate XRD scans of the less-ideal 32 nm/8nm/32 nm YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayercontaining a higher concentration of c-axis grains. FIG. 21A illustratesa θ⁻² θ scan and FIG. 21B illustrates an ϕ scan of the 102 family ofpeaks at χ=56.8° (red) and χ=33.2° (blue) of this less ideal trilayerindicate that it contains a volume fraction of 84% a-axisYBa₂Cu₃O_(7-x).

FIG. 22 illustrates a representative cross-sectional HAADF-STEM image ofthe less-ideal 32 nm/8 nm/32 nmYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayer showing increasedroughness, c-axis and a-axis domains as well as YBa₂Cu₄O_(8-x) stackingfaults (dark lines), and a cubic (Y,Ba)CuO_(3-x) buffer layer. The redarrows mark the c-axis domain that starts from the bottom cubic(Y,Ba)CuO_(3-x) layer. The orange arrows indicate some of theYBa₂Cu₄O_(8-x) stacking faults (features with darker contrast). The graydouble-ended arrows mark the width of examples of 90° in-planerotational twins in which the c-axis is oriented into the plane of theimage. The thickness of the cubic-(Y,Ba)CuO_(3-x) buffer layer is 11±2nm.

FIG. 23A illustrates a low-magnification cross-sectional HAADF-STEMimage of the same less-ideal 32 nm/8 nm/32 nmYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayer exhibitingincreased roughness. Individual YBa₂Cu₃O_(7-x) and PrBa₂Cu₃O_(7-x)layers are separated using dashed lines and the pink arrows indicate thenominal interfaces. FIG. 23B illustrates the high-magnification scan ofa representative region demonstrates fairly abrupt interfaces andYBa₂Cu₄O_(8-x) stacking faults as marked with orange arrows that eitheroriginate from the underlying YBa₂Cu₃O_(7-x) or PrBa₂Cu₃O_(7-x) layers.FIGS. 23C-23E illustrates atomically resolved Pr-M_(5,4) edge (red),Y-L_(3,2) edge (green), and Ba-M_(5,4) edge (blue) elemental mapsevidencing the sharp chemical abruptness of the interfaces. FIG. 23Fillustrates the RGB overlay and FIG. 23G illustrates the simultaneouslyacquired ADF-STEM image showing this same region highlighted by the tanrectangle in FIG. 23A.

Example 2

An example of achieving low surface roughness for a-axis XBCO inaccordance with various implementations of the invention, and theevaluation of such a-axis XBCO is described in a document entitled“a-axis YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers withsubnanometer rms roughness,” and in a document entitled “SupplementaryMaterial, a-axis YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayerswith subnanometer rms roughness,” (collectively “Smoothness Documents”)each of which was included as Appendix Y of U.S. Provisional ApplicationNo. 63/105,230, entitled “A-axis Josephson Junctions with ImprovedSmoothness,” filed on Oct. 24, 2020, which is one of the priorityapplications incorporated above. Growth temperature profile 800 and itsassociated temperatures appear to differ from corresponding profiles andtemperatures in the Smoothness Documents because temperatures of growthtemperature profile 800 are thermocouple temperatures whereas thetemperatures described in the Smoothness Documents are pyrometertemperatures. As would be appreciated, these are two entirely differentways to measure temperature with each having its own inaccuracies.Despite the appearances due to different measurement sensors/techniques,actual temperatures are entirely consistent with one another.

In this example, a-axis YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)trilayers are grown on (100) LaAlO₃ substrates with improved interfacesmoothness. The trilayers are synthesized by ozone-assistedmolecular-beam epitaxy. The thickness of the PrBa₂Cu₃O_(7-x) layer isheld constant at 8 nm and the thickness of the YBa₂Cu₃O_(7-x) layers isvaried from 24 nm to 100 nm. X-ray diffraction measurements show alltrilayers to have >95% a-axis content. The rms roughness of the thinnesttrilayer is <0.7 nm and this roughness increases with the thickness ofthe YBa₂Cu₃O_(7-x) layers. The thickness of the YBa₂Cu₃O_(7-x) layersalso affects the transport properties: while all samples exhibit anonset of the superconducting transition at and above 85 K, the thinnersamples show wider transition widths, ΔT_(c). High-resolution scanningtransmission electron microscopy reveals coherent and chemically sharpinterfaces, and that growth begins with a cubic (Y,Ba)CuO_(3-x)perovskite phase that transforms into a-axis oriented YBa₂Cu₃O_(7-x) asthe substrate temperature is ramped up.

YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers with 24 nm, 32nm, 64 nm, and 100 nm thickYBa₂Cu₃O_(7-x) layers, in which thePrBa₂Cu₃O_(7-x) layer thickness is kept constant at 8 nm, were grown on10 mm×10 mm (100)-oriented LaAlO₃ substrates by ozone-assisted MBE asillustrated in FIG. 9A. Although high quality a-axis YBa₂Cu₃O_(7-x)films have been grown on (100) LaSrGaO₄ substrates, (100) LaAlO₃substrates were used here to identify a path that can be scaled to largediameters to enable its translation to a viable technology. 3-inchdiameter LaAlO₃ substrates are currently available; in the past, even4-inch diameter LaAlO₃ substrates were commercially produced.

The YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers weresynthesized in a Veeco GEN10 MBE. Yttrium (99.6%), barium (99.99%),praseodymium (99.1%), and copper (99.99%) were evaporated from thermaleffusion cells with fluxes of 1.1×10¹³ cm⁻² s⁻¹, 2.2×10¹³ cm⁻² s⁻¹, and3.3×10¹³ cm⁻²s⁻¹, respectively. Prior to growth, the (100) LaAlO₃substrates (CrysTec GmbH) were etched in boiling water, annealed at1300° C. in air for 10 hours, and then etched again in boiling water, toobtain an AlO₂-terminated surface with a step-and-terrace morphology.Following this surface treatment, the backside of the (100) LaAlO₃substrates were coated with a 10 nm thick titanium adhesion layerfollowed by 200 nm of platinum, enabling the otherwise transparentsubstrates to be radiatively heated during MBE growth. TheYBa₂Cu₃O_(7-x) (or PrBa₂Cu₃O_(7-x)) layers were grown by simultaneouslydepositing yttrium (or praseodymium), barium, and copper onto the heatedsubstrate under a continuous flux of distilled ozone (˜80% O₃+20% O₂)yielding a background pressure of 1×10−6 Torr. After growth, the sampleswere cooled to under 100° C. in the same pressure of distilled ozone inwhich they were grown before turning off the ozone molecular beam andremoving the samples from vacuum.

Because YBa₂Cu₃O_(7-x) is a point compound that is unable to accommodateappreciable off-stoichiometry, flux calibration presents a significantchallenge where secondary impurity phases nucleate easily andsignificantly degrade film quality. As discussed above, the flux of eachelement was separately calibrated by growing binary oxides of theconstituents, namely Y₂O₃, PrO₂, BaO, and CuO. From these separatebinary flux calibrations, the temperatures of the effusion cellscontaining yttrium, barium, praseodymium, and copper was adjusted tomatch the desired 1:2:3 flux ratio among Y(Pr):Ba:Cu. The temperature ofthe substrate was measured during growth by a thermocouple (T_(Tc)) thatwas positioned close to, but not in direct contact with the substrate,and by an optical pyrometer (T_(Pyr)) operating at a wavelength of 1550nm. The growth of the trilayers started at low-temperature, T_(Tc)≈420°C. (T_(Pyr)≈530° C.), resulting in a cubic perovskite (Y,Ba)CuO_(3-x)phase for the first few layers and ended at T_(Tc)≈570° C. (T_(Pyr)≈620°C.) following a temperature-ramping procedure. Details of the fluxcalibration method (including the characterization of individual binaryoxides) are illustrated in FIGS. 14-18 . The temperature-ramping detailsand the in-situ reflection high-energy electron diffraction (RHEED)characterization of a reference a-axis YBa₂Cu₃O_(7-x) single-phase filmgrown as part of the optimization of the growth procedure areillustrated in FIG. 19 .

During growth, the films were monitored by in-situ RHEED with KSA-400software and a Staib electron gun operating at 13 kV and 1.45 A. RHEEDimages taken during the growth of the 24 nm YBa₂Cu₃O_(7-x)/8 nmPrBa₂Cu₃O_(7-x)/24 nm YBa₂Cu₃O_(7-x) trilayer are illustrated in FIGS.9B-9G. The structural quality and the a-axis/c-axis ratio of the sampleswas explored using a PANalytical Empyrean x-ray diffractometer (XRD) at45 kV and 40 mA with Cu Kai radiation (1.54057 Å). For surfacemorphological characterization of the films, ex situ atomic forcemicroscopy (AFM) measurements were conducted using an Asylum Cypher ESEnvironmental AFM system. Resistance as a function of temperaturemeasurements were carried out using a homemade four-point van der Pauwgeometry system that slowly dips the samples into a Dewar of liquidhelium.

Detailed investigations of the films were conducted usingatomic-resolution scanning transmission electron microscopy (STEM).Cross-sectional TEM specimens were prepared by focused ion beam (FIB)lift-out with a Thermo Fisher Helios G4 UX Dual Beam system. The sampleswere imaged on an aberration-corrected FEI Titan Themis at 300 kV. STEMhigh-angle annular dark-field (HAADF) imaging was performed with a probeconvergence semi-angle of 21.4 mrad and inner and outer collectionangles from 68-340 mrad. STEM electron energy loss spectroscopy (EELS)measurements were performed on the same Titan system equipped with a 965GIF Quantum ER and Gatan K2 Summit direct detector operated in electroncounting mode, with a beam current of ˜50 pA and scan times of 2.5 or 5ms per 0.4 Å pixel. A multivariate weighted principal component analysisroutine (MSA Plugin in Digital Micrograph) was used to decrease thenoise level in STEM data.

FIG. 9A illustrates the YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)trilayers grown on (100) LaAlO₃ substrates. FIGS. 9B-9G illustratereal-time RHEED images acquired along the [010] azimuth of the (100)LaAlO₃ substrate during the growth of the 24 nm YBa₂Cu₃O_(7-x)/8 nmPrBa₂Cu₃O_(7-x)/24 nm YBa₂Cu₃O_(7-x) trilayer at the six differentlevels illustrated in FIG. 9A. FIG. 9B illustrates the RHEED patternfrom the bottom YBa₂Cu₃O_(7-x) layer; FIG. 9C illustrates the RHEEDpattern at the YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x) interface; FIGS. 9D-9Eillustrate the RHEED pattern for the PrBa₂Cu₃O_(7-x) layer at differentgrowth levels; FIG. 9F illustrates the RHEED pattern at thePrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) interface; and FIG. 9G illustrates theRHEED pattern at the top YBa₂Cu₃O_(7-x) layer. The red arrows added toFIGS. 9B and 9G point to the diffraction streaks associated with thec-axis of the YBa₂Cu₃O_(7-x) lying in-plane.

The structural quality of the samples was assessed by XRD measurements.Generally, FIGS. 10A-10C illustrate X-ray diffraction ofYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers with 24 nm, 32nm, 64 nm, and 100 nm thick YBa₂Cu₃O_(7-x) layers. In FIG. 10A, θ⁻² θscans of the trilayers show only h00, 0k0, and 00χ reflections. In FIG.10B, off-axis 102 reflection ϕ scans at χ=56.6° (red) and χ=33.4° (blue)of the trilayer with 24 nm thick YBa₂Cu₃O_(7-x) layers showing theabsence of c-axis grains. In FIG. 10C, RSM around the LaAlO₃ 1 03reflection (pseudocubic) of this same trilayer with 24 nm thickYBa₂Cu₃O_(7-x) layers showing the a-axis and b-axis orthorhombic 30 3 /31 0 and 033/ 1 30 reflections of YBa₂Cu₃O_(7-x), as well as theperovskite (Y,Ba)CuO_(3-x) 103 reflection. The positions of these filmreflections are indicated by the “+” symbols and dashed ellipses nearthe corresponding reflection labels.

In the coupled θ-2θ XRD scans in FIG. 10A, only h00, 0k0, and 00χreflections of the YBa₂Cu₃O_(7-x) and PrBa₂Cu₃O_(7-x) phases wereindexed, indicating that the film only contains phases with the desiredstoichiometry; they were free of impurity phases associated withoff-stoichiometry. With increasing YBa₂Cu₃O_(7-x) layer thicknesses, 00χreflections emerged showing the nucleation and propagation of c-axisgrains in the films. Off-axis ϕ scans of the 102 family of reflectionsof the orthorhombic YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x) at χ=56.6° andχ=33.4° were used to measure the a-axis and c-axis content of theorthorhombic grains, respectively. Note that χ=90 aligned thediffraction vector to be perpendicular to the plane of the substrate. Inthe 102 ϕ scan of the trilayer sample illustrated in FIG. 10B, fourpeaks associated with the a-axis grains were observed corresponding to90° in-plane rotational twinning: the c-axis of the YBa₂Cu₃O_(7-x) andPrBa₂Cu₃O_(7-x) was aligned parallel to the [010] direction of the (100)LaAlO₃ substrate in one set of twin domains and parallel to the [001]direction of the (100) LaAlO₃ substrate in the other set of twindomains. No intensity associated with c-axis grains was observedindicating that the film contained no c-axis grains within theresolution of our XRD scan. The off-axis ϕ scans of all trilayer samplesillustrated in FIGS. 18A-18D indicate that all four trilayers have morethan 95% a-axis content in the Y(Pr)Ba₂Cu₃O_(7-x) orthorhombic phase. Inaddition to the orthorhombic phases, a cubic perovskite phase was alsoobserved. This phase has been previously reported in the literature as alow-temperature, kinetically-stabilized/-centered cubic phase orprimitive simple-cubic phase. The formation of this phase and its rolein stabilizing the a-axis YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)trilayers is discussed below in tandem with its observation byHAADF-STEM. In the reciprocal space map (RSM) around the LaAlO₃ 103reflection (pseudocubic) in FIG. 10C, a perovskite-like 103 reflection(denoted p-(Y,Ba)CuO_(3-x)) and the orthorhombic phase 303/310 and033/130 reflections associated with the a-axis and b-axis YBa₂Cu₃O_(7-x)grains, respectively, were observed.

The surface morphologies of the same as-grownYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers were establishedby ex situ AFM in tapping mode. With increasing YBa₂Cu₃O_(7-x) layerthickness, the elongated YBa₂Cu₃O_(7-x) grains as well as the in-plane90° rotational twinning of these rectangular-shaped features becamevisible in the 2 μm×2 μm topography scans as illustrated in FIGS.11A-11E. FIGS. 11A-11E generally illustrates surface morphology of theYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers revealed by AFM.FIGS. 11A-11D illustrate 2 μm×2 μm topography scans of the 24 nm/8 nm/24nm, 32 nm/8 nm/32 nm, 64 nm/8 nm/64 nm, and 100 nm/8 nm/100 nm trilayersin tapping mode, respectively. FIG. 11E illustrates rms roughnesscalculated from FIG. 11A-11D as a function of the YBa₂Cu₃O_(7-x) layerthickness. The dotted line serves as a guide for the eye.

The surface morphology arose from the much slower growth rate ofYBa₂Cu₃O_(7-x) grains along [001] than in the (001) plane. Theroot-mean-square (rms) roughness also increased with increasingYBa₂Cu₃O_(7-x) layer thickness from 0.62 nm in the thinnest 24 nm/8nm/24 nm trilayer to 2.3 nm in the thickest 100 nm/8 nm/100 nm trilayer.Surface roughness is an important metric affecting the yield andelectrical performance of YBa₂Cu₃O_(7-x) -based JJs involving extrinsicinterfaces, i.e., tunnel barriers. The 0.62 nm rms roughness observed isthe smoothest reported in the literature and a significant reductionfrom the 11.3 nm previously known on a-axisYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x) bilayers with 270 nm thick YBa₂Cu₃O_(7-x)layers grown on (100) LaAlO₃ substrate.

FIGS. 12A-12C generally illustrate the transport properties of the sameYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers. As is evidentfrom the resistance versus temperature (R-T) plots in FIG. 12A, alltrilayers were found to superconduct. As illustrated in FIG. 12B, thenormal state resistance decreased and the onset temperature of thesuperconducting transition (T_(onset)) increased with increasingYBa₂Cu₃O_(7-x) layer thickness from 85 K for the 24 nm/8 nm/24 nmtrilayer to 90 K for the 100 nm/8 nm/100 nm trilayer. (The dashed linesin FIGS. 12B-12C are guides to the eye). T_(onset) refers to thetemperature at which the resistance falls below a linear extrapolationof the R vs. T behavior from its slope in the 200-300 K regime. Thesuperconducting transition width (ΔT_(c)), referred to here as thetemperature difference between T_(onset) and the temperature at whichthe resistance is zero (within the noise of our measurement), ΔT_(c),decreased with increasing YBa₂Cu₃O_(7-x) layer thickness from 29 K forthe 24 nm/8 nm/24 nm trilayer to 10 K for the 100 nm/8 nm/100 nmtrilayer, as illustrated in FIG. 12C. Compared to c-axis YBa₂Cu₃O_(7-x)films, however, these transition widths are still relatively broad. Suchbehavior is ubiquitous in twinned a-axis YBa₂Cu₃O_(7-x) films especiallywhen the thickness of the a-axis YBa₂Cu₃O_(7-x) is under 100 nm. Thismay arise from local disorder and inhomogeneities in the samples,insufficient oxidation, or from the degradation of the samples overtime.

Two trilayer samples were studied with cross-sectional high-resolutionSTEM to reveal the microstructure and interface abruptness of thesamples as illustrated in FIGS. 13A-13G. FIG. 13A illustrates alow-magnification cross-sectional HAADF-STEM image of the 24 nm/8 nm/24nm YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayer revealing themicrostructure and interface abruptness at the atomic scale. IndividualYBa₂Cu₃O_(7-x) and PrBa₂Cu₃O_(7-x) layers are separated using dashedlines and the pink arrows indicate the interfaces. FIG. 13B illustratesa high-magnification scan of the area highlighted by the orangerectangle in FIG. 13A, demonstrating that the interfaces are fullycoherent. FIGS. 13C-13E illustrate atomically resolved Pr-M_(5,4) edge(red), Y-L_(3,2) edge (green), and Ba-M_(5,4) edge (blue) elementalmaps, respectively, evidencing the sharp chemical abruptness of theinterfaces. FIG. 13F illustrates the RGB overlay and FIG. 13Gillustrates the simultaneously acquired ADF-STEM image of the sameregion, outlined by the tan rectangle in FIG. 13A.

A low-magnification HAADF-STEM image of the 24 nm/8 nm/24 nmYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayer, illustrated inFIG. 13A, is representative of the complete sample. Individual layersare distinguished as darker and brighter regions due to the atomicnumber (Z) contrast of HAADF imaging. The PrBa₂Cu₃O_(7-x) layer givesbrighter contrast compared to the YBa₂Cu₃O_(7-x) layer becausepraseodymium (Z_(Pr)=59) is heavier than yttrium (Z_(Y)=39). The LaAlO₃substrate also shows relatively bright contrast for the same reason(Z_(La)=57). A higher magnification image, illustrated in FIG. 13B,focusing on a representative interface region reveals that theinterfaces in the YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayerare coherent. In neither low-magnification nor in high-magnificationscans were c-axis grains observed in these STEM images, consistent withthe high volume fraction of a-axis growth measured by XRD. Nevertheless,structural coherence does not prove chemical abruptness at interfacesinvolving cuprate high-emperature superconductors.

The chemical abruptness of theYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) interfaces were assessedby atomic-resolution elemental mapping via STEM-EELS. FIGS. 13C-13Eillustrate the elemental maps obtained using Pr-M_(5,4) (red), Y-L_(3,2)(green), and Ba-M_(5,4) (blue) edges in the region outlined by the tanrectangle in FIG. 13A. A red, green, blue (RGB) overlay of the elementalmaps from this region is illustrated in FIG. 13F, while FIG. 13Gillustrates the simultaneously acquired ADF-STEM image of the sameregion. Atomic-resolution EELS maps reveal abrupt interface profiles,corroborating the STEM-HAADF images. Both interfaces show minimal Y—Printermixing, although some asymmetry of the interface profiles is seen.The lower YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x) interface shows a nearlyperfect interface profile free of Y—Pr intermixing; the upper interface(PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)) presents a slightly rougher localprofile with a roughness limited to 1-2 monolayers.

The roughness of the interfaces revealed by STEM and STEM-EELS in FIGS.13A-13G is consistent with the qualitative observations made duringgrowth by in situ RHEED (FIGS. 9B-9G) of this sameYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayer. The arrowedstreaks of a-axis oriented YBa₂Cu₃O_(7-x) in FIG. 9B promptly disappearin transitioning from the lower YBa₂Cu₃O_(7-x) layer to thePrBa₂Cu₃O_(7-x) barrier layer in FIG. 9C, indicating that thePrBa₂Cu₃O_(7-x) barrier layer uniformly covers the lower YBa₂Cu₃O_(7-x)layer. At the upper interface, however, it takes noticeably longer forthe arrowed streaks of the upper YBa₂Cu₃O_(7-x) layer to reappear (FIGS.9F and 9G). Further, the time that it takes for the arrowed streaks ofa-axis oriented YBa₂Cu₃O_(7-x) to reappear in going from thePrBa₂Cu₃O_(7-x) barrier to the YBa₂Cu₃O_(7-x) upper layer takesprogressively longer for the thicker trilayers. This is consistent withthe increased surface roughness seen by AFM in FIGS. 11A-11E as thethickness of the YBa₂Cu₃O_(7-x) layers increases.

In addition to the coherent and chemically sharp interfaces, somedefects were observed by STEM. For example, intergrowths of an extraCu—O layer intercalated into the YBa₂Cu₃O_(7-x) structure to locallyform YBa₂Cu₄O_(8-x) (FIGS. 20A-20D) are seen. Such intergrown layers arewell-known and common in YBa₂Cu₃O_(7-x) in bulk, thin-films, andheterostructures.

The cross-sectional HAADF-STEM imaging also unveiled the location of thecubic perovskite(Y,Ba)CuO_(3-x) phase detected in the XRD measurements.The thickness of the cubic (Y,Ba)CuO_(3-x) layer is found to be 10 nmand it is located under the bottom YBa₂Cu₃O_(7-x) layer (FIG. 20A). Thiscubic (Y,Ba)CuO_(3-x) layer forms at the start of growth when thesubstrate is coldest and surface diffusion is most constrained. Yttriumand barium are unable to diffuse sufficiently far to establish theY—Ba—Ba— . . . ordered arrangement found in the unit cell ofYBa₂Cu₃O_(7-x); instead yttrium and barium share the A-site of theresulting perovskite structure, with copper on the B-site.⁴⁷

As the temperature of the substrate is ramped, the diffusion lengthsincrease, and in-plane structural order emerges. The resulting a-axisYBa₂Cu₃O_(7-x) grains grow epitaxially in one of two symmetry equivalentorientations: with the c-axis parallel to either [010] or [001] of thecubic (Y,Ba)CuO_(3-x) layer on which they nucleate on the (100) LaAlO₃substrate. One set of such domains is clearly seen in FIGS. 20A-20D: theset with the c-axis along the horizontal direction of the image. Theother set, with the c-axis oriented into the plane of the image, aremore difficult to establish because their spacing along the horizontaldirection is the same perovskite spacing as the cubic (Y,Ba)CuO_(3-x)layer on which they nucleated.

The 10 nm thick cubic (Y,Ba)CuO_(3-x) layer is believed to only lieunder the a-axis oriented YBa₂Cu₃O_(7-x) layer and the regions in whichthis perovskite structure appears to extend further, i.e., through andall the way to the surface of the trilayer, are actually the set ofa-axis domains oriented with the c-axis running into the plane of theimage. This is consistent with the grain size of the a-domains seen inthe AFM images in FIGS. 11A-11D as well as published by others fora-axis YBa₂Cu₃O_(7-x) grown on (100) LaAlO₃. From the XRD-scans (FIG.10B and FIG. 18 ), there is an equal volume fraction of both 90°in-plane rotation twin variants, and although the volume sampled in thisSTEM investigation is small, this is also consistent with STEMobservations. Once the substrate temperature is sufficiently high thatthe a-axis YBa₂Cu₃O_(7-x) grains nucleate, both twin variants continuethrough the entire YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)trilayer.

Lastly, additional cross-sectional STEM investigations were performed ona less-ideal 32 nm/8 nm/32 nm sample in order to gain insights on theeffect of c-axis grains in the trilayers. XRD shows the sample chosen tocontain a higher volume fraction (16%) of c-axis orientedYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x) (FIG. 21 ) and to have a higher rmsroughness than the 32 nm/8 nm/32 nmtrilayer characterized in FIGS. 10-12. HAADF-STEM imaging (FIG. 22 ) of this less-ideal 32 nm/8 nm/32 nmtrilayer confirms the presence of c-axis oriented grains in thestructure and also demonstrates the rougher interfaces. Although theinterfaces are rougher, STEM-EELS (FIG. 23 ) shows that they remainchemically abrupt. These results, when evaluated together, explain therougher surfaces of the thicker samples. The c-axis grain formation inthe bottom YBa₂Cu₃O_(7-x) layer not only disturbs the PrBa₂Cu₃O_(7-x)layer (and interface) profiles, but also directly influences the topsurface roughness with changes in the local structural homogeneity inthe first layers of the growth. The strong correlation between surfaceroughness and the volume fraction of c-axis grains in a-axisYBa₂Cu₃O_(7-x) films has been previously noted. To avoid c-axis orientedYBa₂Cu₃O_(7-x), growth is initiated at a substrate temperature whereonly cubic (Y,Ba)CuO_(3-x) can nucleate.

In summary, a-axis YBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x)trilayers were grown with improved structural quality. By leveraging atemperature-ramping procedure that begins with a cubic (Y,Ba)CuO_(3-x)buffer layer, high-quality a-axis trilayers were grown as confirmed byex-situ XRD measurements. AFM investigations revealed the improvedsurface quality with rms roughness that is less than for the thinnestYBa₂Cu₃O_(7-x)/PrBa₂Cu₃O_(7-x)/YBa₂Cu₃O_(7-x) trilayers. STEM analysesunveiled the interrelation between c-axis oriented regions and surfaceroughness. Resistivity vs. temperature (R-T) measurements exhibited anonset of the superconducting transition at T_(onset) 85 K and also thewidening of the superconducting transition width with decreasingYBa₂Cu₃O_(7-x) film thickness. Sharp and coherent interfaces withlimited elemental intermixing are evidenced by atomic-resolutionHAADF-STEM and STEM-EELS. These findings demonstrate that precisecontrol of the growth conditions results in sharp interfaces and smoothsurfaces required in a-axis-based YBa₂Cu₃O_(7-x) heterostructures, e.g.,Josephson Junctions and other oxide electronics.

Example 3

In some implementations of the invention, various fabrication techniquesare utilized to enhance operation and testing of the various JosephsonJunctions described above. In some implementations of the invention, anion mill etching depth is decreased to intentionally leave some PBCOinsulator on top of the bottom YBCO layer. In some implementations ofthe invention, an ion mill etching angle is decreased to decrease adepth of any damage to the bottom YBCO layer introduced by the ion mill.In some implementations of the invention, an additional, largerJosephson Junction is connected in series with the Josephson Junctionunder test to act as a short to the bottom YBCO layer in implementationswhere PBCO covers the bottom YBCO; the larger Josephson Junction thusprovides an indirect connection to the bottom YBCO layer. In someimplementations, two or more of the fabrication techniques mentionedabove are used in combination with one another as would be appreciated.

For example, in a trilayer comprised of 640 angstroms (Å) of YBCO (i.e.,the top YBCO layer), 80 Å of PBCO, and 640 Å of YBCO (i.e., the bottomYBCO layer) on a LAO substrate, an ion mill etch rate was determined tobe roughly 2 Å/s with an ion mill etch angle set at 90° (i.e.,straight-on impact). In some implementations, in a first etching step ofthe trilayer, the ion mill etch angle may be set at 90° to remove thetop YBCO layer; this etch angle provides the best aspect ratio, therebymost accurately transferring a photolithography pattern at the expenseof some ion damage to the underlying material. In some implementations,in a second etching step of the trilayer, the PBCO layer is etched at an“off angle” (i.e., an angle less than 90°) in an effort to ensurecomplete removal of the top YBCO layer without introducing additionalion damage to the bottom YBCO layer. In some implementations, the offangle ranges between 30° and 70°. In some implementations, the off angleranges between 40° and 60°. The etching parameters are provided in Table3 in accordance with various implementations of the invention. Theseparticular etching parameters may be specific to an ion mill being used,and may not be universally applicable to other ion mills or otheretching tools as would be appreciated.

TABLE 3 Etching Parameters Etch Etch Impact Rate Time depth Step Angle(Å/s) (s) (Å) 1 90° 2 312 640 2 50° 2 30 60

In this example, a measurement of T_(c) on the bottom YBCO layer coveredwith PBCO indicated an open circuit, thereby verifying an intactinsulating PBCO layer over the bottom YBCO layer. In addition, AFM wasused to accurately measure a total amount of material removed for step 1and 2 combined as approximately 700 Å; though some ion damage beyond thePBCO layer into the bottom YBCO layer may still be possible. FIG. 24illustrates an R-T curve for the top YBCO layer (in a YBCO/PBCO/YBCOtrilayer) confirming presence of a critical temperature, T_(c), andhence, transition of this top YBCO layer to a superconducting state.This R-T curve confirms that the etching parameters did not negativelyimpact this top layer.

However, leaving the bottom YBCO layer covered with PBCO makes a directelectrical contact with the bottom YBCO layer extremely difficult, ifnot impossible (which is why T_(c) on the bottom layer measured as anopen circuit). To combat this, in some implementations of the invention,the bottom YBCO layer was indirectly contacted via a relatively largesecondary Josephson Junction (e.g., 400 μm×400 μm). FIG. 27B illustratesthe larger secondary Josephson Junction (illustrated as JJ-2) indirectlycontacted to the bottom YBCO layer of the smaller Josephson Junctionunder test (illustrated as JJ-1). As illustrated, each JosephsonJunction under test is coupled in series to the larger JosephsonJunction. (For the sake of completeness, prior testing relied on aninitial testing configuration illustrated in FIG. 27A which requireddirect electrical contact with the bottom YBCO layer, which contact isno longer possible in implementations with a covering layer of PBCO.)

As would be appreciated, a larger Josephson Junction will have a muchlarger I_(c) in comparison to the smaller Josephson Junction, andtherefore (ideally) stay in its superconducting state even as thesmaller Josephson Junction transitions to its resistive state. (See,e.g., FIG. 26 .) In essence, the larger Josephson Junction acts as asuperconducting wire connecting to the bottom YBCO layer through thePBCO, allowing measurements of various characteristics of the smallerJosephson Junction under test. In some implementations of the invention,to ensure that the larger Josephson Junction acts as a superconductingwire, a scaling factor may be greater than 3 (i.e., the larger JosephsonJunction may be 3 times larger in area, or more, than the smallerJosephson Junction under test). As would be appreciated, this scalingfactor may improve the I-V curves of the Josephson Junction under test.In the examples of FIG. 25 , the scaling factors were both less than 3.However, the scaling factor may be increased as the size of the smallerJosephson Junction under test are decreased.

FIG. 25 illustrates an I-V curve confirming operation for each of twoJosephson Junctions (one 350 μm×350 μm and one 250 μm×250 μm), accordingto various implementations of the invention. In some implementations ofthe invention, a size of each of these Josephson Junction may be reducedto roughly 5 μm×5 μm or smaller.

The I-V curves of FIG. 25 illustrate soft transitions fromsuperconducting state to resistive state with a critical current, I_(c),of ˜1 mA, which current is typical of conventional Josephson Junctions.These I-V curves confirm successful contact with both top and bottomYBCO layers in the trilayer, which remained intact during and afterfabrication. FIG. 26 illustrates an ideal I-V curve for operation of aJosephson Junction, with a strong transition between a superconductingand resistive states as would be appreciated. While the criticalcurrents of the I-V curves of FIG. 25 are not as sharply defined as theideal I-V curve in FIG. 26 , subsequent fabrication improvements areexpected to improve these I-V curves. Such fabrication processimprovements may include, but are not limited to, reducing the size ofthe Josephson Junction under test, increasing the scaling factor, andother fabrication improvements.

In some implementations of the invention, ion mill damage may be usedadvantageously to pattern damaged regions as electrical insulation,which is a common fabrication step for semiconductor and superconductorcircuits used to isolate one part of the circuit from another as wouldbe appreciated.

While the invention has been described herein in terms of variousimplementations, it is not so limited and is limited only by the scopeof the following claims, as would be apparent to one skilled in the art.These and other implementations of the invention will become apparentupon consideration of the description provided above and theaccompanying figures. In addition, various components and featuresdescribed with respect to one implementation of the invention may beused in other implementations as would be appreciated.

What is claimed:
 1. A method for fabricating a Josephson Junction out ofa trilayer of YBCO/PBCO/YBCO, the method comprising: etching a top YBCOlayer via ion milling to substantially remove the top YBCO layer; andetching a portion of a PBCO layer via ion milling to completely removethe top YBCO layer and to remove some but not all of the PBCO layer. 2.The method of claim 1, wherein etching a top YBCO layer via ion millingto substantially remove the top YBCO layer comprises etching the topYBCO layer via ion milling at 90° to substantially remove the top YBCOlayer.
 3. The method of claim 1, wherein etching a portion of a PBCOlayer via ion milling to remove any remaining top YBCO layer and toremove some but not all of the PBCO layer comprises reducing any iondamage to a bottom YBCO layer.
 4. The method of claim 1, wherein etchinga portion of a PBCO layer via ion milling to remove any remaining topYBCO layer and to remove some but not all of the PBCO layer comprisesetching the portion of the PBCO layer via ion milling at an off angle.5. The method of claim 4, wherein etching the portion of the PBCO layervia ion milling at an off angle comprises etching the portion of thePBCO layer via ion milling at an angle less than 90°.
 6. The method ofclaim 5, wherein etching the portion of the PBCO layer via ion millingat an angle less than 90° comprises etching the portion of the PBCOlayer via ion milling at an angle between 30° and 70°.
 7. The method ofclaim 5, wherein etching the portion of the PBCO layer via ion millingat an angle less than 90° comprises etching the portion of the PBCOlayer via ion milling at an angle between 40° and 60°.